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Q. The maximum wavelength of radiation emitted at $900\, K$ is $4 \,\mu m$. The maximum wavelength of radiation emitted at $1200\, K$, will be :

BHUBHU 2002

Solution:

From Wien's displacement law
$\lambda_{m} T=$ constant
where $\lambda_{m}$ is the maximum wavelength emitted and $T$ is absolute temperature.
$ \lambda_{1} \,T_{1} =\lambda_{2}\, T_{2}$
$\Rightarrow 4 \times 900 =1200 \times \lambda_{2} $
$\Rightarrow \lambda_{2} =\frac{4 \times 900}{1200}=3 \,\mu m$